1. Field of the Invention
The present invention relates to the field of fine structures characterized by magnetic resonance and to a method for processing magnetic resonance signals.
2. Prior Art
U.S. Pat. No. 7,932,720 describes a method for measurement of biologic textures too fine to be resolved by conventional magnetic resonance imaging, providing a quantitative measure of the characteristic spatial wavelengths of these textures. In its simplest form the method consists of acquiring finely-sampled spatially-encoded magnetic resonance echoes along an axis of a selectively-excited inner-volume positioned within the biologic tissue to be analyzed. Signal analysis yields spectra of textural wavelengths within various sub-regions along the spatially encoded axis of the selected tissue volume.
Filtering techniques have been used in the prior art to selectively analyze sub-regions (regions of interest) by windowing within the selectively excited internal volume but they are non-linear as the method involves taking the magnitude of the signal to produce a signal intensity as a function of location. This prior art method (U.S. Pat. No. 7,932,720) describes a method wherein the basic steps are as follows:                1. Subject the sample to a magnetic field;        2. Subject the sample to magnetic resonance excitation;        3. Receive an echo signal from the sample while the sample is subjected to a magnetic field gradient;        4. Fourier transform the echoes and take the magnitude to convert them into a signal intensity versus position,        5. Select a region of interest by multiplying the transformed data by a windowing function;        6. Fourier transform again, converting back into the echo domain;        7. Display the result as the magnitude of the resulting derived spectrum treating it as a measure of frequency content.        
While the approach in the '720 patent provides insight into underlying structure, particularly for biological samples, it is limited due to being non-linear and restricted to the use of the nonlinear magnitude function and two Fourier transforms.
Other prior art methods based on magnetic resonance for analyzing fine textures are similar to that of the '720 patent in that they also are nonlinear as a result of taking the magnitude to generate a signal intensity vs. location. They differ from the '720 patent in that they are based on the analysis of magnetic resonance image data rather than a one dimensional signal intensity. In general the steps used by these methods are as follows:                1. Receive a multiplicity of echoes (as a result of a 2D or 3D magnetic resonance acquisition sequence),        2. Fourier transform and then take the magnitude of the echoes to convert them into a signal intensity versus position (i.e., create an image or a set of images),        3. Select a region of interest by multiplying the transformed data by a windowing function (wherein the shape and the width have been carefully chosen to optimize the signal extraction without introducing truncation artifacts, and to minimize the decrease in spectral resolution),        4. Use a Fourier or other transform again to convert back into the echo domain which is a measure of frequency content,        5. Display the result as the magnitude of the resulting derived spectra.        